Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > sssucid | Structured version Visualization version Unicode version |
Description: A class is included in its own successor. Part of Proposition 7.23 of [TakeutiZaring] p. 41 (generalized to arbitrary classes). (Contributed by NM, 31-May-1994.) |
Ref | Expression |
---|---|
sssucid |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssun1 3776 | . 2 | |
2 | df-suc 5729 | . 2 | |
3 | 1, 2 | sseqtr4i 3638 | 1 |
Colors of variables: wff setvar class |
Syntax hints: cun 3572 wss 3574 csn 4177 csuc 5725 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-v 3202 df-un 3579 df-in 3581 df-ss 3588 df-suc 5729 |
This theorem is referenced by: trsuc 5810 suceloni 7013 limsssuc 7050 oaordi 7626 omeulem1 7662 oelim2 7675 nnaordi 7698 phplem4 8142 php 8144 onomeneq 8150 fiint 8237 cantnfval2 8566 cantnfle 8568 cantnfp1lem3 8577 cnfcomlem 8596 ranksuc 8728 fseqenlem1 8847 pwsdompw 9026 fin1a2lem12 9233 canthp1lem2 9475 nosupbday 31851 nosupbnd1 31860 nosupbnd2lem1 31861 limsucncmpi 32444 finxpreclem3 33230 clsk1independent 38344 suctrALT 39061 suctrALT2VD 39071 suctrALT2 39072 suctrALTcf 39158 suctrALTcfVD 39159 suctrALT3 39160 |
Copyright terms: Public domain | W3C validator |